Method and device for frequency response measurement

ABSTRACT

A method is provided for measuring a frequency response of an object, the method involving: generating an excitation signal having relatively fast changing frequency, defined by a time-domain function; generating at least one reference signal, having a waveform corresponding to the excitation signal; introducing the excitation signal into the object, receiving a response signal from the object; analyzing said response signal in a signal analyzer by correlating the response signal with at least one reference signal during a relatively short sliding time-domain window.

BACKGROUND OF THE INVENTION

1. Technical field

The invention relates to measurement techniques, particularly to thefield of measurement of the frequency response. For example, included inthis field are electrical network and vector-impedance analyzers whichmeasure the transfer coefficient as a function of the frequency. Theinvention can be used in bio-impedance measurement devices for medicaldiagnosis, in testers of electrical and electronics circuits, inanalyzers of electrochemical elements for their condition monitoring,for investigating of materials by their electrical properties (e.g.,conductivity) and also for many other applications.

2. Background art

Solutions are known, where the transfer coefficient of the circuit ismeasured by applying an excitation signal (e.g., of sinusoidal waveform)to the measured circuit and by multiplying and accumulating of theresponse signal waveform to this excitation signal, or in other words,by correlating (which is a practical equivalent to mathematicalconvolution) of these signals, and carried out, in digitalimplementation, by multiply-and-accumulate (MAC) unit. Also second,quadrature (90 degrees shifted, from excitation signal) reference signalfor second correlation (quadrature result component) could be used (U.S.Pat. No. 7,428,683). Correlation calculation can often include alsonormalization of the result, taking into account average levels andamplitudes (intensities) of the signals.

Such solution is also described in the paper, “FPGA-Based AnalogFunctional Measurements for Adaptive Control in Mixed-Signal Systems”,JIE QIN et al, August 2007, for BIST, the device consisting ofnumerically controlled oscillators, digital-to-analog converter andanalog-to-digital converter and adjusted for applying excitation signalto an object (e.g., circuit under test and reading back the responsesignal from the object, and numerical multiplier and accumulator toanalyze the properties of the object under test. The disadvantage ofsuch solutions is that the result is calculated by correlation of thereference and response signals as one integral value over the fullmeasurement cycle and therefore such measurement is not showing thetransfer coefficient separately for individual frequencies (that means,frequency response) and secondly, such integral measurement is notreflecting correctly and in real-time dynamical, changing in timecircuit or object.

For measurement of the frequency response, including dynamic (fastchanging in time) circuits and objects, the technical solutions areknown, where wideband, e.g., chirp excitation signal are used, and theresponse signal is analyzed in relatively short slidingtime-domain-window by frequency analysis, e.g., by short-time Fourier'transform (STFT) or by wavelet analysis, as described in U.S. Pat. No.6,885,960 and U.S. Pat. No. 5,797,840.

The closest solution known in the art is described in the paper“Influence of the analyzing window on electrode impedance measurement bythe continuous frequency scanning method”, K. Darowicki, P. Slepski,Journal of Electroanalytical Chemistry, Vol 533, Issues 1-2, 20 Sep.2002, pp 25-31. In this solution a linear chirp signal is generated foran excitation signal. For dynamical time and frequency domain analysis,a combined time-frequency analysis in the form of short-time Fouriertransform (STFT) is used, in which Fast Fourier Transform (FFT) is usedin a relatively short-time sliding window, while this window could beweighted by the Gauss window function.

The disadvantage of this solution is the complexity of combinedtime-frequency analysis of the response signal, as a very sophisticatedfull spectral Fourier analysis is carried out in every short-timewindow, demanding a huge processing power and much computing time forcalculations. This limits significantly the usage of such solutions forreal-time monitoring of the objects and circuits, because and forlimited by computational power of processors, which in its turn islimited by cost and available power.

Thus, there is a need for new improved method and device for frequencyresponse measurements

Disclosure of the Invention

Objective of the invention is to simplify the measurement of thefrequency response, what in turn allows to use cheaper, simplerelectronic devices with lower power consumption. Another objective isimproved accuracy of frequency response measurements in time orfrequency domain.

The objective of the invention is achieved by the invented method,comprising generating an excitation signal having relatively fastchanging frequency, defined by a time-domain function, generating atleast one reference signal having waveform corresponding to saidexcitation signal, introducing said excitation signal into the object,receiving a response signal from said object, analyzing said responsesignal in a signal analyzer by correlating said response signal withsaid at least one reference signal during a relatively short slidingtime-domain window.

The relatively short time window can be further divided into severalindependent sliding sub-windows. The analysis could be performeddigitally in one implemented correlation of the excitation signal and areference signal, which could be the excitation signal itself It isreasonable to use a second, quadrature channel to determine the second(quadrature, imaginary) component of the response signal, e.g., thefirst and second reference signals, generated as sine and cosine wavechirp signals, respectively.

Alternative is to use Hilbert Transform to get the quadrature(imaginary) reference waveform from the first reference waveform.

As excitation signals, the linear, logarithmic or exponential chirpsignals can be used for linear, logarithmic or exponentialrepresentation of the frequency response correspondingly. Alsoarbitrarily changing frequency could be used in some applications, e.g.,for measurement of very specific frequency response shapes, wherespecific frequencies under interest are known (e.g., for eddy currentmeasurement and validation of electrical properties of metals and metalproducts such as coins, when often discrete frequencies (e.g., 120, 240and 480 kHz) are used for measurement). Furthermore, by adaptivechanging the frequency dependency function of the excitation signal, orparameters of the analysis window, it is possible to classify the objectunder test with minimum computational and signal processing needs andachieve so the maximal processing speed, making so the proposed solutionalso preferable to monitor the objects with fast changing parameters.

Also, as typically measurements are carried out periodically, it ispossible, according to the current measurement results (e.g., dependingon the measured values and dispersion of the results in specificfrequency regions), to improve the measurement accuracy and decrease thefluctuations (e.g., caused by noise) of the measurements, by adaptivelychanging the amplitude of the excitation signal and the length ofanalysis window for specific frequency regions or values.

By shape of the waveform both sine waves and non sine waves (e.g.,square waves) can be used. Preferably, the beginning and ending of theshort time-window are selected at zero-crossing time-instants of theexcitation signal. Preferably the time-window duration is adjustedaccording to the running frequency of the signal, thus e.g., using forlower frequencies a longer time-window.

Alternative to usage of the two quadrature against each other referencewaveforms, is to use only one, the first reference waveform,corresponding to the excitation signal waveform, by transforming thereceived response signal by Hilbert transform, to the complex responsesignal containing both direct (real) and imaginary parts and thenperforming the complex correlation with the first reference signals,getting a complex transfer functions for time instants and relatedfrequency values, according to the sliding of the time domain window.

BRIEF DESCRIPTION OF THE DRAWINGS

The essence of the invention is described in FIG. 1, as a block-diagramfor an example of the implementation of the invention.

Example of carrying out the invention

One embodiment of the invention shown on FIG. 1 comprises a unit ofsignal generation and data acquisition 1 for generating of theexcitation signal, comprising a sine chirp waveform buffer (orgenerator) 2 and a cosine chirp waveform buffer (or generator) 3 (orother signals with relatively fast changing frequency). Waveformgeneration buffers are to be initialized with arrays of values,corresponding to the waveform, at the initialization of the wholesystem. In the generated waveform, the instance values of the frequencyhave to change relatively fast. The output of the sine chirp waveformbuffer is connected, through digital-analog converter 5 (and anadditional driver, if needed) into an device to be tested (DUT) 6 withunknown time variant transfer function K (t, f). It can be appreciatedthat instead of device, any other object with can be tested such aselectrical or electronics circuits, biological objects (e.g., inbio-impedance measurements for medical diagnosis), electrochemicalelements, and materials). The response signal is acquired from theobject through analog-digital converter (ADC) 7 (if needed, afteramplification and conditioning, not shown) into a response signalwaveform buffer 4 and is further processed in a correlation unit 9 forinphase component K_real(t, f), using sine chirp as reference signal,and in a correlation unit 10 for quadrature component K_imag(t, f),using cosine chirp as reference signal. Multiply-and-accumulate (MAC)units can be used as correlation units 9 and 10 in processing signals indigital form.

Further, a relatively short time-domain sliding window, e.g., weightedby Gauss function window, which could be initialized into array ofvalues h(t) into a sliding window h(t) buffer 8, is applied for analysisof the response signal. In the scope and with weights of the window theresponse signal is convolved by the reference sine and cosine wavechirps to calculate the real and imaginary parts of the response signal.As the excitation signal value is known, the transfer function of thecircuit (object) under test can be calculated from this result, for thetime instance (and thus, for a specific frequency). Further, a parameterof the object under investigation, e.g., unknown impedance part of thecircuit can be calculated. The mentioned short-time window is slidingsynchronously in all the mentioned waveform buffers: sine and cosinewave reference buffers and response signal buffer. So the value oftransfer coefficient is defined just for corresponding to the slidingwindow position (time and frequency values) position.

Preferably chirp-signals are used, where the frequency of the signal ischanging linearly or logarithmically in time, giving so linear orlogarithmic frequency response function. Of course, other timedependences of the frequencies can be used, depending on the applicationand on which frequency-domain resolution is currently needed.

Instead the sine and cosine waveform signals in some applicationsnon-sinusoidal waveforms, e.g., square wave signals, can be used. Suchsignals are easier to generate and simpler to use for correlationcalculation.

Measurement could be performed in steps, by using adaptively at everystep the results of the previous step for defining the parameters of theexcitation signal or the analysis window.

Corresponding adaptive parameters of the excitation signal or of theanalysis window can be defined for minimizing the effect of noise andmeasurement errors.

Corresponding adaptive parameters of the excitation signal or of theanalysis window can be defined to identify an object, e.g., as 1 eurocoin, 2 euro coin, or to distinguish real coin from forged coin, or toclassify the measured object, e.g., by “pass” or “not pass”, e.g., in aproduction process.

Of course, the mentioned waveforms of cosine and sine wave signals couldbe generated, and the response signal waveform processed, withoutbuffers by using known analog-to-digital signal processing techniques.

Analog-to-digital and digital-to-analog converters are needed for thedigital implementation of the solution (e.g., when using a digitalsignal processor). In analog solution, these converters are not neededand in correlation calculation the accumulation of multiplicationresults is changed by integration of the multiplication results.

The length of the time-domain sliding window can be implemented asdynamically and adaptively variable, being for lower frequencies longer.Preferably the beginning and ending of the sliding time-domain windoware synchronized by zero-crossings of the excitation signal, sodecreasing the spectral leakage of analysis, as integer number ofperiods of the signal is included in the analysis window.

The sliding time-domain window can consist of several sub-windows. Forexample, when the frequency dependence of time has the same instantvalue of frequency at various time instances, e.g., if the sameexcitation signal (burst) includes positive and negative chirp signalsequences. As the same frequency is at both positive and negative partsof the chirp, the analysis window can consist of one sub-window from thepositive and the other from the negative part of the chirp.

1. A method for measuring a frequency response of an object, the methodcomprising: generating an excitation signal having relatively fastchanging frequency, defined by a time-domain function; generating atleast one reference signal, having a waveform corresponding to saidexcitation signal; introducing said excitation signal into the object,receiving a response signal from said object; analyzing said responsesignal in a signal analyzer by correlating said response signal withsaid at least one reference signal during a relatively short slidingtime-domain window.
 2. The method as in claim 1, wherein said relativelyshort sliding time-domain window is divided into several time-domainsub-windows.
 3. The method as in claim 1, wherein the length of saidrelatively short sliding time-domain window is variable and determinedby running frequency value.
 4. The method as in claim 1, wherein thebeginning and the end of said relatively short sliding time-domainwindow are chosen at zero-crossings of said excitation signal.
 5. Themethod as in claim 1, wherein said excitation signal is generated as asinusoidal wave.
 6. The method as in claim 1, wherein the excitationsignal is generated as non-sinusoidal wave.
 7. The method as in claim 6,wherein said excitation signal is a square wave signal.
 8. The method asin claim 1, wherein the excitation signal is generated as a chirpsignal.
 9. The method as in claim 8, wherein said chirp signal is alinear chirp signal.
 10. The method as in claim 8, wherein said chirpsignal is a nonlinear chirp signal.
 11. The method as in claim 10,wherein said nonlinear chirp signal is selected from the groupconsisting logarithmic, exponential and arbitrarily formulated chirpsignal.
 12. The method as in claim 1, comprising analyzing said responsesignal in at least two consecutive steps, while using adaptively resultsof an earlier step for determining the parameters of said excitationsignal or at least one analysis window for a subsequent step.
 13. Themethod as in claim 12, wherein in said previous step the parameters ofthe excitation signal or of at least of one analysis window for thesubsequent step are defined to minimize the effect of noise ormeasurement inaccuracy.
 14. The method as in claim 12, wherein in saidprevious step the parameters of said excitation signal or of at leastone analysis window for the subsequent step are defined to classify saidobject.
 15. The method as in claim 1, wherein said reference signals areconvolved in complex arithmetic in said short time-domain window by saidresponse signal for calculation of the real and imaginary parts of theresponse signal, to be used for calculation of the real and imaginaryparts of the object's transfer coefficient as a function of thefrequency.
 16. The method as in claim 1, wherein a first referencewaveform corresponding to said excitation signal, is used to determinereal and imaginary parts of a transfer coefficient by correlating it inthe short-time window by complex representation of said response signal,given by Hilbert Transform of the acquired response signal.
 17. A devicefor measuring of the frequency response of an object, comprising: a unitof signal generation and data acquisition for generating an excitationsignal with a fast changing frequency to be introduced into said objectand a response-signal analyzer adapted to receive a response signal fromsaid object, said response-signal analyzer working in a short timewindow, wherein the analyzer comprises a first unit adapted to generatea first reference waveform that is in phase with the excitation signal,and a second unit adapted to generate a second reference waveform thatis in quadrature with the excitation signal, wherein the waveforms ofthe first and second excitation signals are defined by said excitationsignal waveform, and means for correlating said response waveform withthe first reference waveform and with the second reference waveform in ashort time-domain window.